Some Russian experts say it's a measure of how quickly unusual things can happen in a political system in which a single figure, Mr. Putin, holds so many strings of power in his hands.

The prevailing view in Moscow is that the bilateral US-Russia agenda is too badly stalemated, especially on the critical issue of missile defense, for any breakthroughs to occur in what most agree is an increasingly troubled relationship. In this view, Putin is just going through the motions of making nice with the newly reelected Mr. Obama, and no one should expect anything more than a few photo ops and well-meaning rhetoric from the meeting, whose date has yet to be set.

But others argue that fresh and dramatic departures may be coming, and that people should have guessed it last March when an open mic at a Seoul, South Korea, meeting caught Obama telling then-President Dmitry Medvedev to ask Putin to "give me space" until after the November US presidential election. "This is my last election," Obama told Mr. Medvedev. "After my election I have more flexibility."

"Now the elections are over, and [Putin and Obama] can move on to the next stage," says Sergei Markov, vice rector of the Plekhanov Economic University in Moscow and a frequent Putin adviser in the past.

"Putin views Obama soberly, and sees him as a man who keeps his promises. Obama realizes that Putin has very strong capacities of leadership; in other words, he's a man who can make deals," Mr. Markov adds. "The bad period in our relationship is over, and there are objectively very good possibilities for a new beginning."

"The current US president is someone you can do business with; he is a man who listens to other people’s arguments, knows how to communicate and can take decisions. We do not always agree, but if he adopted decisions he ultimately implemented them," Medvedev, now prime minister, told Finnish journalists Tuesday.

"I hope that he will adopt the same approach during his second term," he said.

"Disagreements between the US and Russia on the bilateral agenda are too deep-seated and complicated to allow for any big breakthroughs, no matter how friendly the coming meeting between Obama and Putin may turn out to be," says Sergei Strokan, a foreign affairs columnist with the liberal Moscow daily Kommersant.

"It comes down to mutual trust, which is absent. Putin may wish to build a better relationship with Obama, but many of the things he does work the opposite way.... You may say we no longer needed USAID or Nunn-Lugar, but the abrupt ending of those projects produced a very bad taste, and undeniably hurt the actual, existing relationship. Putin may feel like he needs to change the atmospherics, show that he's a democratic leader and not an isolated autocrat. But it's just going through motions," Mr. Strokan says.

There are other straws in the wind that suggest Putin may be seeking to cultivate a more liberal image. After months of tightening screws on Russia's internal opposition, Putin suddenly sent out a softer signal Monday by telling the Kremlin's newly reconfigured Human Rights Council that he would review draconian new laws that would force foreign-funded nongovernmental groups to register as "foreign agents" – due to come into effect next week – as well as a law drastically increasing penalties for "defamation," a bill currently before the State Duma that would effectively criminalize blasphemy, and other measures that triggered widespread concerns.

One thing all experts agree on, it is Putin who sets the tone and makes all the key decisions in Russia.

"During Putin's election campaign earlier this year, he played the anti-American card in his rhetoric quite a lot," says Markov.

"He did that for good reasons. Most of the Russian public is suspicious of the US and its intentions, and Putin also wanted to discredit some of his political opponents as being too pro-Western. It worked, but now Putin feels it's time for a course correction," he adds.

"It's also true that Obama, being under attack from Mitt Romney for being too soft on Russia, had to limit his movements in the direction of Moscow. But now we're past all that. Both men are free to act. You will see things happen."